Analysis
# Load data
d3cp <- read.csv('C:\\Users\\millerry\\Downloads\\analysisTasks3.csv')
d3n <- read.csv('C:\\Users\\millerry\\Downloads\\analysisTasksNoEngage3.csv')
#d3cp <- read.csv('C:\\Users\\Ryan M\\Downloads\\analysisTasks3.csv')
#d3n <- read.csv('C:\\Users\\Ryan M\\Downloads\\analysisTasksNoEngage3.csv')
# Manually remove repeats
d3n <- d3n[-which(d3n$DaqName %in% c("20130612092744.csv", "20140104105417.csv")),]
d3cp <- d3cp[-which(d3cp$DaqName %in% c("20130612092744.csv", "20140104105417.csv")),]Visuals
Standard deviation of lane deviation by dosage group and secondary task engagement:
Conclusions: - Not much difference when deriving engagement segment using changepoint detection vs. using entire period task is available - We can still analyze the data both ways, but will use the changepoint detection approach for now
Boxplot version:
Conclusions: - Standard Deviation of Lane Deviation is much higher when engaged in secondary task (artist-menu search) - Similar differences across experimental conditions - This visual ignores pairing of segments/participants
Paired (trt/control) version:
Conclusions: - Within each experiment condition individual subject performance is worse when engaged in secondary task
Within Subject Performance Differences by Condition
Tables
Secondary task segments available for analysis for each of the 19 subjects:
| XM | XP | YM | YP | ZM | ZP | Sum | |
|---|---|---|---|---|---|---|---|
| Subject ID 3 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 7 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 10 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 15 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 17 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 18 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 21 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 25 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 26 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 29 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 31 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 32 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 34 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 35 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 104 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 113 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 120 | 3 | 3 | 3 | 3 | 3 | 3 | 18 |
| Subject ID 123 | 3 | 3 | 3 | 2 | 3 | 3 | 17 |
| Subject ID 129 | 2 | 3 | 3 | 3 | 3 | 3 | 17 |
| Sum | 56 | 57 | 57 | 56 | 57 | 57 | 340 |
Marginally, there is a statistically significant effect of secondary task engagement (for most Dose/Event combos) on standard deviation of lane deviation (p-values are from paired t-tests within subject/event):
| DosingLevel | EventID | mean_SDL | sd_SDL | n | p_value | signif |
|---|---|---|---|---|---|---|
| XM | 1 | -0.1079823 | 0.6653311 | 19 | 0.47929 | |
| XM | 2 | 0.3852318 | 1.0004674 | 18 | 0.10234 | |
| XM | 3 | 0.6290988 | 0.9803059 | 19 | 0.00515 | ** |
| XP | 1 | 0.3818299 | 0.8399112 | 19 | 0.04753 | * |
| XP | 2 | 0.1759859 | 1.4630276 | 19 | 0.60005 | |
| XP | 3 | 0.4446652 | 0.8482441 | 19 | 0.02231 | * |
| YM | 1 | 0.2406506 | 0.9370421 | 19 | 0.26295 | |
| YM | 2 | -0.1298222 | 1.3342822 | 19 | 0.67149 | |
| YM | 3 | 0.4220633 | 0.7426300 | 19 | 0.01324 | * |
| YP | 1 | 0.4575804 | 0.8007496 | 19 | 0.01274 | * |
| YP | 2 | 0.5653850 | 1.1621832 | 18 | 0.03902 | * |
| YP | 3 | 0.3885585 | 0.7604960 | 19 | 0.02594 | * |
| ZM | 1 | 0.2998543 | 1.0046808 | 19 | 0.19328 | |
| ZM | 2 | 0.0252731 | 1.0177404 | 19 | 0.91380 | |
| ZM | 3 | 0.6257512 | 0.8121137 | 19 | 0.00078 | *** |
| ZP | 1 | 0.4451658 | 1.0555926 | 19 | 0.06603 | . |
| ZP | 2 | 0.5386620 | 1.0042601 | 19 | 0.01939 | * |
| ZP | 3 | 0.4225396 | 0.6069259 | 19 | 0.00241 | ** |
Models
Model 1 - Base Model
\[y_{ij} = \beta_0 + \gamma_i + \beta_1 SecTask_{ij} + \beta_2 DoseXM_{ij} + \beta_3 DoseYM_{ij} + \ldots + \epsilon_{ij}\]
- \(y_{ij}\) = Standard Deviation of lane deviation for subject \(i\) at dosing level \(j\)
- \(\gamma_i\) = subject specific random intercept
- \(SecTask_{ij}\) = dummy variable indicating observation measures performance during secondary task (1 = sec task, 0 = control segment)
- \(DoseAA_{ij}\) = dummy variable for dose = “AA” (1 = specified dose, 0 = reference group)
- In our models we will re-define the reference group such that all dose effects are positive
d3cp$Dose_Grp <- relevel(d3cp$DosingLevel, ref = "ZP")
fit <- lmer(data = d3cp, SD.Lane.Deviation ~ Dose_Grp + Experiment + (1 | ID))
fit_sum <- summary(fit)
kable(round(fit_sum$coefficients, 4))| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 0.4598 | 0.0853 | 171.3511 | 5.3935 | 0.0000 |
| Dose_GrpXM | 0.0154 | 0.1012 | 655.1849 | 0.1522 | 0.8790 |
| Dose_GrpXP | 0.0756 | 0.1007 | 654.9280 | 0.7502 | 0.4534 |
| Dose_GrpYM | 0.0873 | 0.1007 | 654.9280 | 0.8665 | 0.3865 |
| Dose_GrpYP | 0.0517 | 0.1012 | 655.1849 | 0.5109 | 0.6096 |
| Dose_GrpZM | 0.0454 | 0.1007 | 654.9280 | 0.4507 | 0.6524 |
| Experiment | 0.3443 | 0.0583 | 654.9280 | 5.9029 | 0.0000 |
kable(round(anova(fit), 4))| Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) | |
|---|---|---|---|---|---|---|
| Dose_Grp | 0.6434 | 0.1287 | 5 | 655.0996 | 0.2226 | 0.9528 |
| Experiment | 20.1476 | 20.1476 | 1 | 654.9280 | 34.8437 | 0.0000 |
This model suggests a significant effect of secondary task engagement on standard deviation of lane deviation, but no impact of experimental condition
- A few problems with it:
- Doesn’t adjust for differences in speed
- Skewed distribution of
SD.Lane.Deviation - Treats all 3 secondary tasks as the same
- It also isn’t looking for effect modification by
Dose_Grp
Model 2 - Log-transformed outcome, control for eventNum and Avg.Speed
fit <- lmer(data = d3cp, log2(SD.Lane.Deviation) ~ relevel(DosingLevel, ref = "XM") +
factor(eventNum) + Avg.Speed + Experiment + (1 | ID))
kable(round(summary(fit)$coefficients, 4))| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | -3.9636 | 0.5686 | 370.8770 | -6.9712 | 0.0000 |
| relevel(DosingLevel, ref = “XM”)XP | 0.1522 | 0.1954 | 652.9692 | 0.7789 | 0.4363 |
| relevel(DosingLevel, ref = “XM”)YM | 0.2630 | 0.1976 | 657.7072 | 1.3311 | 0.1836 |
| relevel(DosingLevel, ref = “XM”)YP | 0.1300 | 0.1964 | 653.7328 | 0.6617 | 0.5084 |
| relevel(DosingLevel, ref = “XM”)ZM | 0.3465 | 0.1972 | 657.0216 | 1.7573 | 0.0793 |
| relevel(DosingLevel, ref = “XM”)ZP | 0.0550 | 0.1969 | 656.3927 | 0.2792 | 0.7802 |
| factor(eventNum)2 | 0.4422 | 0.1426 | 664.1713 | 3.1003 | 0.0020 |
| factor(eventNum)3 | 0.3166 | 0.1417 | 662.7813 | 2.2341 | 0.0258 |
| Avg.Speed | 0.0288 | 0.0087 | 402.0684 | 3.3167 | 0.0010 |
| Experiment | 0.7464 | 0.1124 | 652.2426 | 6.6397 | 0.0000 |
kable(round(anova(fit), 4))| Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) | |
|---|---|---|---|---|---|---|
| relevel(DosingLevel, ref = “XM”) | 9.1783 | 1.8357 | 5 | 655.6375 | 0.8545 | 0.5115 |
| factor(eventNum) | 21.6956 | 10.8478 | 2 | 659.0886 | 5.0497 | 0.0067 |
| Avg.Speed | 23.6309 | 23.6309 | 1 | 402.0684 | 11.0003 | 0.0010 |
| Experiment | 94.7050 | 94.7050 | 1 | 652.2426 | 44.0854 | 0.0000 |
Model 3 - Log-transformed outcome, control for eventNum and Avg.Speed, test for effect modification
- Does
Dose_Grpmodify the performance deteroration seen during secondary tasks?
fit <- lmer(data = d3cp, log2(SD.Lane.Deviation) ~ relevel(DosingLevel, ref = "ZP") +
factor(eventNum) + Avg.Speed + Experiment +
relevel(DosingLevel, ref = "ZP"):Experiment + (1 | ID))
kable(round(summary(fit)$coefficients, 4))| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | -3.9386 | 0.5590 | 387.3314 | -7.0460 | 0.0000 |
| relevel(DosingLevel, ref = “ZP”)XM | 0.0083 | 0.2779 | 649.4002 | 0.0297 | 0.9763 |
| relevel(DosingLevel, ref = “ZP”)XP | 0.0782 | 0.2778 | 650.6645 | 0.2814 | 0.7785 |
| relevel(DosingLevel, ref = “ZP”)YM | 0.2091 | 0.2754 | 647.3339 | 0.7593 | 0.4479 |
| relevel(DosingLevel, ref = “ZP”)YP | 0.1210 | 0.2795 | 651.8014 | 0.4329 | 0.6652 |
| relevel(DosingLevel, ref = “ZP”)ZM | 0.4550 | 0.2754 | 647.2304 | 1.6523 | 0.0990 |
| factor(eventNum)2 | 0.4430 | 0.1430 | 659.1465 | 3.0971 | 0.0020 |
| factor(eventNum)3 | 0.3175 | 0.1421 | 657.7581 | 2.2334 | 0.0259 |
| Avg.Speed | 0.0286 | 0.0087 | 398.7192 | 3.2839 | 0.0011 |
| Experiment | 0.8304 | 0.2754 | 647.2321 | 3.0158 | 0.0027 |
| relevel(DosingLevel, ref = “ZP”)XM:Experiment | -0.1252 | 0.3911 | 647.2303 | -0.3201 | 0.7490 |
| relevel(DosingLevel, ref = “ZP”)XP:Experiment | 0.0399 | 0.3894 | 647.2418 | 0.1025 | 0.9184 |
| relevel(DosingLevel, ref = “ZP”)YM:Experiment | -0.0024 | 0.3894 | 647.2402 | -0.0063 | 0.9950 |
| relevel(DosingLevel, ref = “ZP”)YP:Experiment | -0.0902 | 0.3911 | 647.2304 | -0.2306 | 0.8177 |
| relevel(DosingLevel, ref = “ZP”)ZM:Experiment | -0.3269 | 0.3894 | 647.2665 | -0.8394 | 0.4015 |
kable(round(anova(fit),4))| Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) | |
|---|---|---|---|---|---|---|
| relevel(DosingLevel, ref = “ZP”) | 8.1640 | 1.6328 | 5 | 649.3536 | 0.7556 | 0.5821 |
| factor(eventNum) | 21.7850 | 10.8925 | 2 | 654.0749 | 5.0409 | 0.0067 |
| Avg.Speed | 23.3021 | 23.3021 | 1 | 398.7192 | 10.7838 | 0.0011 |
| Experiment | 94.6682 | 94.6682 | 1 | 647.2411 | 43.8109 | 0.0000 |
| relevel(DosingLevel, ref = “ZP”):Experiment | 2.5570 | 0.5114 | 5 | 647.2534 | 0.2367 | 0.9463 |
Model 4- Paired Difference as outcome
fit <- lmer(data = df, diff_SD_lane_pos ~ relevel(DosingLevel, ref = "YM") + factor(EventID) + diff_speed + (1 | SubjectID))
kable(round(summary(fit)$coefficients, 4))| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 0.1210 | 0.1562 | 211.2718 | 0.7743 | 0.4396 |
| relevel(DosingLevel, ref = “YM”)XM | 0.1231 | 0.1778 | 312.8555 | 0.6922 | 0.4893 |
| relevel(DosingLevel, ref = “YM”)XP | 0.1565 | 0.1769 | 312.6196 | 0.8849 | 0.3769 |
| relevel(DosingLevel, ref = “YM”)YP | 0.2848 | 0.1778 | 312.7221 | 1.6015 | 0.1103 |
| relevel(DosingLevel, ref = “YM”)ZM | 0.1390 | 0.1776 | 312.9546 | 0.7822 | 0.4347 |
| relevel(DosingLevel, ref = “YM”)ZP | 0.2910 | 0.1770 | 312.6593 | 1.6443 | 0.1011 |
| factor(EventID)2 | -0.0315 | 0.1305 | 315.2556 | -0.2413 | 0.8095 |
| factor(EventID)3 | 0.2020 | 0.1279 | 314.3777 | 1.5790 | 0.1153 |
| diff_speed | -0.0004 | 0.0178 | 330.3307 | -0.0235 | 0.9813 |
kable(round(anova(fit),4))| Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) | |
|---|---|---|---|---|---|---|
| relevel(DosingLevel, ref = “YM”) | 3.3992 | 0.6798 | 5 | 312.8148 | 0.7622 | 0.5776 |
| factor(EventID) | 3.6341 | 1.8170 | 2 | 314.1180 | 2.0372 | 0.1321 |
| diff_speed | 0.0005 | 0.0005 | 1 | 330.3307 | 0.0006 | 0.9813 |